Problem: Solve for $x$ and $y$ using elimination. ${-4x+5y = 17}$ ${x-3y = -13}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-4x+5y = 17}$ $4x-12y = -52$ Add the top and bottom equations together. $-7y = -35$ $\dfrac{-7y}{{-7}} = \dfrac{-35}{{-7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-4x+5y = 17}\thinspace$ to find $x$ ${-4x + 5}{(5)}{= 17}$ $-4x+25 = 17$ $-4x+25{-25} = 17{-25}$ $-4x = -8$ $\dfrac{-4x}{{-4}} = \dfrac{-8}{{-4}}$ ${x = 2}$ You can also plug ${y = 5}$ into $\thinspace {x-3y = -13}\thinspace$ and get the same answer for $x$ : ${x - 3}{(5)}{= -13}$ ${x = 2}$